Attack Move is a key bind that I came across in the key binding list. From my own testing it seems to move to the target location and attack the nearest target-able object including turrets.

I heard people talking about it in IRC chats and during the casting of Tourney Games. Most pertaining to AD-carries, in particular that Doubleliftt uses it which is the reason he is so fluid. I was just wondering what exactly it is good for and how I could use it to improve my damage out-put as an AD Carry?

If anyone could create a little video tutorial showing instances in how you use this it would be great. It is hard to understand when explained in words how to kite using it for instance. To someone who has never used it before.

5 Answers
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Clarification of the term "click to attack"

There are two key bindings related to attack:

Attack move - default button A - when you click A cursor changes into target pick. Clicking left mouse button then makes your character either attack the picked target or run to the picked location and attack the first target that appears in your range during the movement. If there are more targets, it picks the closest one.

Advantages of using "click to attack"

When you chase into a brush you start attacking immediately when you see the target

When you missclick right button when lasthitting then you go in the creeps and get yourself out of position, that can never happen while using Attack move

When lasthitting, Attack move checks for a target in a slightly larger radius than right click, which makes it easier to pick the target. It also might be an advantage in larger crowds of creeps when you need to select a creep precisely.

Disadvantages

When using Attack move during chasing and clicking it on the ground, then if a different eligible target appears closer, you immediately start attacking it. Therefore, you obviously lose some time and even if it is miliseconds it may change the outcome of the chase.

i do not understand your second point, please rephrase
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GGClassic-Jona52Apr 15 '12 at 23:57

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@GGClassic-Jona52 if you try to right-click on a creep, but you click the ground next to the creep instead of the creep, you will begin to move there. On the other hand, if you attack-move (A) to that same space, you will attack nearby creeps instead of moving into the minions.
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Raven Dreamer♦Apr 16 '12 at 0:10

RClick away from an enemy, then attack move away from them to automatically attack.
Continue this process to run while auto attacking them.
This same process can be done to neutral monsters and even turrets/inhibs.

2) Last hitting

Use the A key as opposed to right clicking on a minion to kill them. This ensures that even if your click misses the minion, you will still auto attack it.

3) Chasing an Enemy into a brush

Attack moving into a brush will ensure you immediately attack them upon gaining vision (As opposed to RClicking them first)

You'll find that attack moving can often shave valuable time off your attacks. It ensures you're getting maximum output of damage and removes the time wasted by human response in clicking on the target manually. It takes a lot of practice to learn when to use it and when to right click. Particularly when the target you wish to hit is not closest to you. I'd highly recommended practicing this as an AD carry.

Going along with what Toast said, Attack-move (a-click) is a mechanic popularized by Starcraft and Warcraft. A-move would allow units to automatically attack all enemies along the way.

Saving Milliseconds

The main advantage to A-moving is that you don't have to move your mouse. The milliseconds it takes to recognize a target and physically move the mouse above it makes a noticeable difference in professional play. Just let the keyboard hand and computer handle it.

For example,

My champion is in the lower-left corner of the screen

Enemy champion is in the middle of the screen

My mouse is in the top-right corner of the screen

And my champion, the enemy champion and my mouse make a straight line. So now I have two choices,

Right-click on the enemy: I need to move my mouse down to the middle of the screen and click within the hit-box of the enemy, about 50 square pixels out of the whole screen. If I miss the hit-box slightly, my champion walks helplessly towards the enemy.

Attack-move: I hit "A" on the keyboard and then I left click where my cursor already was. I didn't have to drag my mouse anywhere. I didn't have to aim my cursor. I saved several milliseconds.

A-moving is especially useful when you are kiting because, by shaving off those milliseconds of mouse movement, you can use a champions attack speed to its full potential while moving.

It's useful in general when you have a good position on your enemy and don't have to retarget it every time,

It's similar to why you would use QWER to cast spells instead of clicking the icons each time.

Doublelift and many other pros may have previously played DOTA, Warcraft or Starcraft where APM optimization is the norm and developed a habit of A-moving.

You got it right with the starcraft/warcraft thing, but what is with the "you dont have to move your mouse"...well obviously, when you click A on keyboard...I dont think you got the idea of the question
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SanthosMay 2 '12 at 6:43

@Santhos Added an example that may clarify why you can save time moving the mouse. Lemme know what you think
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Atav32Jun 1 '12 at 20:53

It is not a bad example, but I still think that this is ok only in a very few cases. You suppose that there is only you and the enemy champion (and only one). Once there is a creep or another champion, you still have to move your mouse closer to the target. The fact is that you dont have to hit the hitbox so precisely as with right click and if you accidentally "miss the click" you wont move to the enemy doing exactly nothing, you will still shoot, but maybe at a wrong (unwanted) target.
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SanthosJun 4 '12 at 22:33

@Santhos Added a note about situations where a-moving is optimal. Thanks for the discussion btw =)
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Atav32Jun 5 '12 at 17:34

Glad to be helpful - I think it is quite to the point right now
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SanthosJun 10 '12 at 14:57

One of the main advantages of this on a ad carry is the fact that wont need to manually select a target amount the chaos going when a team fight starts, late game that is an absolute avantage since every second of the fight that your able to auto attack a target instead of moving around is REALLY important.